The climate system comprises multiple components, primarily the atmosphere, ocean and cryosphere, each incorporating physical processes that interact across scales. To help understand the behaviour of this complex system, and evaluate climate model simulations, researchers typically take a reductionist approach, focusing on individual climate processes and studying their relationships with weather and climate in different regions. While more holistic approaches, such as climate networks, have been developed to explicitly address the complexity of the climate, here we argue for the use of a new approach that accounts for multiple cross‐scale process interactions, framed with respect to specific climate outcomes of societal importance. We introduce and explore the concept of “climate process chains” (CPCs), describing their potential application using examples determined for southern Africa. Building on related theoretical concepts, and through reviewing literature on climate processes and teleconnections to southern Africa, we identify candidate CPCs for two outcomes of societal interest; a regional‐scale drought and local‐scale heavy rainfall. Focusing on such outcomes means that CPC investigations have more relevance to climate risk management contexts, as well as providing a constraint on the exploration of climate uncertainties for a region. We argue that CPCs may help to articulate relationships amongst regionally relevant climate processes across temporal and spatial scales, and discuss their potential utility in climate research, including in the evaluation of climate models and their simulations.